Our diversified lattice strategy combines
exploratory as well as precision studies, moving in different directions in
the space of \(Sp(2N)\)  theories. Aside from the aforementioned desire
to explore other applications of these theories,
even when we restrict attention to the CHM context, there are still two good reasons
to adopt this gradual approach.
First, the CHM candidate proposed in Ref. [1]} is rather unusual,
and there are no reference results in the literature
for comparable theories.
It is hence important to build a whole portfolio of related theories,
against which we can benchmark our results.
The pragmatic reason why this benchmarking is needed,
is that lattice studies with fermions in mixed representations
are technically challenging and resource intensive.
Most of the existing, publicly available lattice
codes developed for other purposes
do not implement multiple dynamical representations—we mentioned above some very recent examples
for the \(SU(4)\)  theories.
Even after the code becomes available, and after testing the correctness of the
behaviour of the algorithms used in the calculations—as we shall demonstrate shortly—one still must
explore the phase space of the lattice theory.
In our case, this is controlled by three bare parameters (the gauge coupling and the two fermion masses),
besides the lattice size, making the mapping of phase transitions quite non-trivial.
Finally, the number of elementary degrees of freedom of the \(Sp(4)\)  theory with
\(N_f=2\)  and \(n_f=3\)  is large, and hence,
while the theory is still asymptotically free,
one expects slow running of the couplings, and possibly the emergence of
large anomalous dimensions, making it more challenging to characterise the theory.
We will
provide evidence of the fact that we can address all of these challenges,
and we can start production
of ensembles giving access to physically relevant regions of parameter space.
